Not sure it’s possible in iOS, but if you open the link in Safari (rather than Twitter in-built browser), you can pull down on the page to unveil a banner to open in YouTube app.
I think that the Twitter app needs to support opening in YouTube app. A different Twitter app might well support this, but the standard one doesn’t seem to.
Actually, reading around, this may be an iOS 13 issue…
@Gothelf, after a bit more experimenting, if you long touch the link and then select “Share Via” and select open in Safari, you will get the link redirected to the YouTube app. You might have to switch off ad-blocker for YouTube site though, if you are running a content blocker. Don’t know if you were already doing that.